1. Field of the Invention
The present invention relates to method for wireless communication; and more particularly, to differential wireless communication using multiple transmitter antennas.
2. Description of Related Art
Fading is one of several physical phenomena that tend to increase error rates, or to reduce channel capacity, in wireless transmission systems. Fading is the result of destructive interference, at the receiver, between correlated signal portions that because of scattering have arrived over different-length paths. Multiple antenna arrays can be used in wireless communication to reduce error rates and increase transmission rates.
In certain fading environments, the theoretical capacity of a multiple-antenna communication link increases linearly with the size of the transmitter or receiver array, this effect being determined by the array having the lesser number of antennas. This effect has been predicted for rich scattering environments in which fading is xe2x80x9cflat.xe2x80x9d That is, the propagation coefficients that describe the effect of the physical transmission channel on the transmitted signal are approximately independent of frequency over the signal bandwidth. Flat fading can be achieved in practice for a particular environment if the bandwidth is not too great, or if it is restricted appropriately.
Significantly, such a linear increase in capacity occurs only if the propagation coefficients between all pairs of transmitter and receiver antennas are known to the receiver. In practice, this condition can be met only if the receiver is trained, from time to time, by receiving known training signals from the transmitter.
Communication methods that use such a training procedure are described, for example, in the co-pending U.S. patent application Ser. No. 08/938,168 now U.S. Pat. No. 6,058,105, commonly assigned herewith, filed Sep. 26, 1997 by B. M. Hochwald et al. under the title, xe2x80x9cMultiple Antenna Communication System and Method Thereof.xe2x80x9d
Other co-pending patent applications, commonly assigned herewith, that describe related subject matter are Ser. No. 08/673,981 now U.S. Pat. No. 6,097,771, filed on Jul. 1, 1996 by G. J. Foschini under the title xe2x80x9cWireless Communications System Having a Layered Space-Time Architecture Employing Multi-Element Antennas,xe2x80x9d Ser. No. 09/060,657 now U.S. Pat. No. 6,317,466, filed on Apr. 15, 1998 by G. J. Foschini and G. D. Golden under the title xe2x80x9cWireless Communications System Having a Space-Time Architecture Employing Multi-Element Antennas at Both the Transmitter and Receiver,xe2x80x9d and a patent application filed on Jul. 10, 1998 by T. L. Marzetta under the title xe2x80x9cDetermining Channel Characteristics in a Space-Time Architecture Wireless Communication System Having Multi-Element Antennas.xe2x80x9d
Unfortunately, training intervals cut into the available time during which data may be transmitted. The length of this interval increases as the number of transmitter antennas is increased. Moreover, the propagation coefficients can be treated as constant only over an average period of time referred to as the fading coherence interval. To be effective, training should be repeated at least once per such interval. However, fading is very rapid in some environments, such as those in which a mobile station is operating within a rapidly moving vehicle. For rapidly fading environments, the time between fades may be too short for the communication system to learn the propagation coefficients belonging to even one transmitting antenna, much less those of a multiple antenna array.
Thus, there remains a need to more fully realize, in practice, the theoretical benefits of multiple antenna arrays in fading environments.
In the co-pending U.S. patent application Ser. No. 09/134,297 now U.S. Pat. No. 6,327,310, commonly assigned herewith, filed on Aug. 14, 1998 by B. M. Hochwald et al. under the title, xe2x80x9cWireless Transmission Method for Antenna Arrays, Having Improved Resistance to Fading,xe2x80x9d there was described a new method of signal modulation. This new method, which we refer to as xe2x80x9cUnitary Space-Time Modulation (USTM),xe2x80x9d is robust against fading and receiver-induced noise in flat fading environments. Significantly, it does not require knowledge of the propagation coefficients, although in some implementations, such knowledge can be used to further improve performance.
In USTM, each message to be transmitted is transformed into a sequence of signals selected from a constellation of L possible signals, L a positive integer. (Thus, each transmitted signal embodies a number of bits given by log L. In the present discussion, xe2x80x9clogxe2x80x9d will denote the binary logarithm.) Each of these symbols is, itself, a time sequence of complex amplitudes for transmission by the transmitting antenna or antennas. The transmissions by all of the antennas in the transmitting array are concerted. All of these transmissions (for a given signal) are made in the same sequence of T successive time units (which we refer to as symbol intervals), T a positive integer.
Thus, a signal may be represented by a complex-valued matrix having T rows and M columns. Each column corresponds to a respective antenna of the transmitting array, and represents the sequence of complex amplitudes to be transmitted by the antenna. Each row corresponds to a particular one of the T symbol intervals, and describes the complex amplitude to be transmitted by each respective antenna during that interval. Such a set of complex amplitudes is referred to as a xe2x80x9csymbol.xe2x80x9d Each symbol is distributed in space (i.e., across the transmitting array), and each signal is composed of T symbols distributed in time.
Significantly, each signal matrix must have the property that all of its columns are orthonormal. (It should be noted in this regard that corresponding to a signal matrix "PHgr", the baseband signals provided to the transmitting array are represented by matrix S, where S={square root over (TP)} "PHgr". Here, P is the average power fed into each antenna.) Because each of these columns has length T, there can be never be more than T such columns that are all orthogonal to each other.
There are L signals, and M columns per signal. Thus, over the entire constellation, there are Lxc3x97M columns. Because there will typically be many signals in the constellation (constellation sizes in the hundreds of thousands, or even more, are desirable in at least some applications), Lxc3x97M will typically be much greater than T. Well known mathematical properties dictate that there can be no more than T mutually orthonormal column vectors. Therefore, it will be unlikely that, given a randomly chosen pair of signal matrices, the columns of one such matrix will be orthogonal to the columns of the other.
If such orthogonality between the respective columns of signal pairs were possible, the probability of confusing one received signal for another would be reduced to its ideal minimum value. Given that this ideal condition is unattainable, it is desirable, instead, to design the signal constellation in such way that correlations between pairs of signal matrices, of a kind that tends to increase the error probability, are made as small as possible.
U.S. patent application Ser. No. 09/134,297 now U.S. Pat. No. 6,327,310, cited above, describes techniques for minimizing these correlations that are most useful when the number M of transmitting antennas is relatively small. Commonly assigned U.S. patent application Ser. No. 09/206,843, filed on Dec. 7, 1998, by B. M. Hochwald et al. under the title, xe2x80x9cWireless Transmission Method for Antenna Arrays Using Unitary Space-Time Signals,xe2x80x9d describes a more powerful technique that can readily generate signal constellations of low correlation when M, L, and T are relatively large, without demanding impractical amounts of computational resources.
Another technique that tends to mitigate the effects of fading is differential phase modulation, in which phase differences carry transmitted information. Although differential phase modulation is a known technique for single-antenna transmission and reception in fading environments, there are no known generalizations of this technique for use with an arbitrary number of antennas.
The method of communication according to the present invention is a method of differential communication for a multiple transmitter array. In the method, a plurality of baseband signals are generated. Each baseband signal includes one or more sequences, in time, of complex numbers, each sequence to be transmitted from a respective antenna of the multiple transmitter antenna array. Each baseband signal is representable as a transmission matrix in which each column represents a respective antenna and each row represents a respective time segment. Each transmission matrix is generated based on input data and a previous transmission matrix representing a previously transmitted baseband signal.
The baseband signals are modulated on a carrier to form transmit carrier-level signals, and the transmit carrier-level signals are transmitted by the multiple transmitter antenna array.
Receive carrier-level signals are received by at least one antenna at the receiver end. Each of the receive carrier-level signals are formed from the transmit carrier-level signals passing through a channel. The receive carrier-level signals are demodulated to form a plurality of receive baseband signals. Each receive baseband signal includes one or more receive sequences, in time, of complex numbers. Each receive baseband signal is representable as a reception matrix in which each column represents a respective receiver antenna and each row represents a respective time segment. Each reception matrix depends on data encoded therein and a previous reception matrix representing a previously received receive baseband signal. The receive baseband signals are processed to obtain data represented thereby.